my understanding is that inorganic fertilisers wash out of soil and compost easily, so there'd be little point in doing this. whereas nutrients in decomposing plant matter and soils are much less liable to washing out. i have read scientific explanations for this but cannot repeat it accurately.
if it's loss of Nitrogen that you're worried about - well that's not a problem as so long as you have green sappy plant matter to put on your heap you will be adding plenty of N. if you really can't get any and you only have dry woody matter in your compost heap you could
pee on it instead to add lots of N. one thing that can take N out of compost piles is turning it - some N gas will escape. so you could not turn it if you are worried about that.
there will be some weeds in your area that are rich in Potassium, probably, look them up and throw them on.
i think it's a shame to use inorganic fertilisers which have been extracted from other parts of the world when we have most nutrients we need all around us.